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Steel Designers' Manual - 6th Edition (2003)
ditional deflection limits based on a proportion of the beam span may not be appropriate.
The absolute deflection may also be important and pre-cambering may need
to be considered for beams longer than 10 m.
Elastic section properties, as described in section 21.6.1, are used in establishing
the deflection of composite beams. Uncracked section properties are considered to
be appropriate for deflection calculations. The appropriate modular ratio is used,
but it is usually found that the section properties are relatively insensitive to the
precise value of modular ratio. The effective breadth of the slab is the same as that
used in evaluating the bending resistance of the beam.
The deflection of a simple composite beam at working load, where partial shear
connection is used, can be calculated from: 13
dc¢= dc + 051 . ( -K)
( ds - dc)
for propped beams ¸
˝
(21.18)
d¢= d + 031 . ( -K)
( d - d ) for unpropped beams˛
c c s c
Basic design 625
where dc and ds are the deflections of the composite and steel beam respectively at
the appropriate serviceability load; K is the degree of shear connection used in the
determining of the plastic strength of the beam (section 21.7.4). The difference
between the coefficients in these two formulae arises from the different shearconnector
forces and hence slip at serviceability loads in the two cases. These formulae
are conservative with respect to other guidance. 10
The effect of continuity in composite beams may be considered as follows. The
imposed load deflection at mid-span of a continuous beam under uniform load or
symmetric point loads may be determined from the approximate formula:
dcc = d¢
c( 1- 0. 6( M1+ M2) M0)
(1.19)
where d¢c is the deflection of the simply-supported composite beam for the same
loading conditions; M0 is the maximum moment in a simply-supported beam subject
to the same loads; M1 and M2 are the end moments at the adjacent supports of the
span of the continuous beam under consideration.
To determine appropriate values of M1 and M2, an elastic global analysis is carried
out using the flexural stiffness of the uncracked section.
For buildings of normal usage, these support moments are reduced to take into
account the effect of pattern loading and concrete cracking. The redistribution of
support moment under imposed load should be taken as the same as that used at
the ultimate limit state (see Table 21.1), but not less than 30%.
For buildings subject to semi-permanent or variable loads (e.g. warehouses), there
is a possibility of alternating plasticity under repeated loading leading to greater
imposed load deflections. This also affects the design of continuous beams designed
by plastic hinge analysis, where the effective redistribution of support moment
exceeds 50%. In such cases a more detailed analysis should be carried out considering
these effects (commonly referred to as ‘shakedown’) as follows:
(1) evaluate the support moments based on elastic analysis of the continuous beam
under a first loading cycle of dead load and 80% imposed load (or 100% for
semi-permanent load);